answer c,d, e, f only - please and thank you.

Problem 3. A shop with three furniture makers produces uniquely designed chairs and sofas from fabric and wood. The requirements for each piece are as follows: Fabric/vd 3 8 Chair Sofa Wood/units) 6 5 Labor(hr) 9 4 For a week's operation, the shop has available 96 yd of fabric, 90 units of wood, and 120 hr of labor. A profit of $70 is realized from the sale of a chair and a profit of S60 from a sofa. (a) Formulate a mathematical model for this example, (b) Show graphically that the solution to the problem calls for the manufacture of 7 chairs and 9 sofas. (c) Consider the weekly production schedule that maximizes profit. How would one implement such a schedule? (d) Possible answer to part (c): Show that the weekly production of 8 chairs and 10 sofas, or of 8 chairs and 9 sofas, or of 7 chairs and 10 sofas is impossible within the given restrictions, but that 7 chairs and 9 sofas can be produced. Thus this feasible schedule, with integral components, appears to be the desired schedule. (e) Show that it is also possible for the shop to produce weekly, within the given limitations, 10 chairs and 6 sofas. Compare the profit associated with this production schedule with the profit of the (7.9) production schedule of part (d). (1) Conclusion: Does the objective functions at corners points produce the optimal solution? If not, what can we do